To explore the possible instabilities and ensuing dynamics of hexagonal patterns in the presence of rotation we investigate a modified Swift-Hohenberg Equation:
The instabilities can be long-wave or short-wave instabilities, steady or oscillatory. Of particular interest is the situation in which hexagons become unstable at all wavelengths as shown in the stability diagram below. In this case there are no stable steady hexagon solutions above R=0.09.
In this regime regular hexagon patterns decay into a persistently changing disordered pattern that has a mixed cellular and stripe-like appearance.
1 work performed with F. Sain